General Relativity and Quantum Cosmology

Title:
Inflationary spacetimes are not past-complete

Abstract: Many inflating spacetimes are likely to violate the weak energy condition, a
key assumption of singularity theorems. Here we offer a simple kinematical
argument, requiring no energy condition, that a cosmological model which is
inflating -- or just expanding sufficiently fast -- must be incomplete in null
and timelike past directions. Specifically, we obtain a bound on the integral
of the Hubble parameter over a past-directed timelike or null geodesic. Thus
inflationary models require physics other than inflation to describe the past
boundary of the inflating region of spacetime.

Comments:

We improve the basic argument to apply to a wider class of spacetimes, use a better title and add a discussion of cyclic models. 4 pages, 1 figure, RevTeX